Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 1.25 m/s
v2 = m/s
2.Easy
12d1​ = 200 mm, v1​ = 0.5 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 0.5 m/s
v2 = m/s
3.Medium
d1​ = 100 mmd2​ = 60 mm12p1​ − p2​ = 51 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 60 mm. The pressure at the inlet is 51 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 60 mmp1 − p2 = 51 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 400 kPad2​ = 25 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 25 mm. In the wide section the pressure is 400 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 25 mmp1 = 400 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 260 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 60 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 260 mm. The discharge coefficient is 0.99. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 100 mmd2 = 60 mmΔh = 260 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 160 kPad2​ = 40 mm, p2​ = ?Δz = 6 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 6 m. At section 1 the pressure is 160 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 160 kPav1 = 2.5 m/sΔz = 6 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 2.813 m/s
  2. 2. v2 = 3.556 m/s
  3. 3. Q = 30.61 L/s
  4. 4. p2 = 390 kPa
  5. 5. Q = 24.05 L/s
  6. 6. p2 = 65.64 kPa

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